Thermal noise random pulse generator and random number generator

ABSTRACT

A random number generator has a simple configuration using know inexpensive electronic parts and can generate the true physical random numbers at a required generation speed. Such a random number generator can provide the true physical random numbers to any sectors of society at dramatically low cost A random pulse generator comprises a thermal noise generating element ( 2 ) having a resistor, a conductor or a semiconductor such as a diode adapted to generate thermal noises Hen no electric current is supplied to them, an analog-amplifier circuit for amplifying the irregular potential generated from the thermal noise generating element and a waveform shaping circuit ( 6 ) adapted to take out the output of the amplifier circuit as random rectangular pulse signals. A thermal noise random number generator comprises, in addition to the above components, an n-bit counter (n being an integer) for measuring the time interval between a random pulse signal output from the waveform shaping circuit ( 6 ) and the immediately succeeding random pulse signal and is adapted to output the count of the n-bit counter as natural random number.

TECHNICAL FIELD

This invention relates to a physical random number generator adapted togenerate the true random numbers by taking out thermal noises generatedfrom a thermal noise generating element such as a resistor or a diodeMen no electric current is supplied to the thermal noise generatingelement and amplifying it by means of an amplifier. A physical randomnumber generator according to the invention can suitably be used forpersonal identification, coding and other purposes in computertelecommunications and mail-order business because it can perfectlyeliminate frauds. A physical random number generator according to theinvention is also suitable for generating the probability in variousgame machines.

BACKGROUND ART

Known physical random number generating methods include those forgenerating random numbers by detecting a random phenomenon of nucleardecay as disclosed in Japanese Patent Applications Laid-Open Nos.11-161473 and 11-184676 filed by the inventor of the present inventionand those for generating random numbers by detecting the light of alight-emitting diode as disclosed in Japanese Patent ApplicationLaid-Open No. 11-145362 also filed by the inventor of the presentinvention.

A number of random number generators designed to supply an electriccurrent to a resistor and utilize thermal noises from the resistor havebeen invented and are described in text books on recording mediums.

While a physical random number generator that utilizes the decayproducts of a radioactive source provides the advantage that it caneasily generate the true random numbers, it is accompanied by a numberof disadvantages including that it involves a complex manufacturingprocess and high manufacturing cost because of the use of a radioactivesource and that a device with radioactive source has difficulty to besocially accepted because of the regulation of radioactivity andenvironmental assessment in the use of radioactive substances.

A physical random number generator adapted to generate random numbers bydetecting the light from a light emitting diode (LED) by means of aphotodiode is advantageous in tat it can generate the true randomnumbers at relatively low cost However, such a physical random numbergenerator needs new technological developments for integrally forming aLED and a photodiode as a compact unit.

It is impossible to enclose a known random number generators designed tosupply an electric current to a resistor in order to utilize it asthermal noise source in a portable card or an integrated circuit (IC)because it requires the use of specifically designed devices including apiece of hardware for generating random numbers and a processing circuitfor removing the 1/f noise that are generated as a result of supplyingan electric current to the noise source.

Therefore, it is the object in the present invention to provide a randomnumber generator that has a simple configuration with known inexpensiveelectronic parts and can generate the true physical random numbers at arequired generation speed. Such a random number generator can providethe true physical random numbers to any industrial fields atdramatically low cost

DISCLOSURE OF INVENTION

The present invention is based on the fact that noises generated from agenerating thermal noise element such as a resistor or a diode when noelectric current is supplying to it are pure thermal noises that do notcontain the so-called 1/f noise that is inversely proportional to thefrequency f, and that the pure thermal noises represent a perfect randomphenomenon. According to the invention, there is provided a random pulsegenerator that utilizes the above phenomenon and is adapted to amplifythermal noises by means of an amplifier to produce random analog pulsesignals, transform the analog pulses into rectangular pulses and takingout the rectangular pulses for use. Thus, a random pulse generatoraccording to the invention supplies random pulse signals that can beused for generating the natural random numbers.

In the second aspect of the invention, random pulses generated from arandom pulse generator according to the invention are taken out as pulsesignals and the time intervals between the random pulse signals and thesucceeding pulse signals that are generated immediately after therespective first random pulse signals are measured and the measuredvalues are supplied as the true physical random numbers. In case of timemeasurement with a n-bit counter, this invention use the measured valueof the n bit number (n: integer, e.g., 8-bits: 0-255) as the truephysical random numbers.

In the third aspect of the invention, the number of random pulses withina predetermined time period generated by a random pulse generatoraccording to the invention are counted and one digit number orseveral-digits number of the counted relative frequency values aresupplied as the true physical random numbers.

In the fourth aspect of the invention, random pulses generated by arandom pulse generator according to the invention are taken out as pulsesignals and the pulse frequencies within a predetermined time period orthe time intervals between the random pulse signals and the succeedingpulse signals that are generated immediately after the respective firstrandom pulse signals are measured so that the pulse peak value of one ofthe measured random pulse signals is selected as threshold value of apulse peak discriminator in order to generate the true random numbers ata required random number generating speed

In the fifth aspect of the invention, a thermal noise generating elementsuch as a resistor or a diode and other electronic circuits arecontained integrally in an IC card or an IC chip provided with aninformation processing circuit and the information processing circuitare fed with physical random numbers for the purpose of personalidentification, encoding and other purposes in computertelecommunications or mail-order business or for using it as aprobability generator in a game machine.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of an embodiment of thermal noise physicalrandom number generator according to the invention, showing its overallconfiguration.

FIG. 2 is a graph showing the pulse peak distribution between the pulsepeak value and the relative frequency obtained in an experiment forvarious different resistance values of the resistor fitted to thethermal noise generating element of the embodiment of the embodiment ofFIG. 1.

FIG. 3 is a graph showing the pulse peak distribution of the randompulses generated by amplifying the thermal noises from the resistor of aresistance of 560kΩ in the embodiment of FIG. 1 showing as obtained inan experiment.

FIG. 4 is a graph showing that the observed frequency distribution ofthe time intervals between the random pulse signals generated byamplifying the thermal noises from the resistor of the embodiment ofFIG. 1 and the succeeding pulse signals that are generated immediatelyafter the respective first random pulse signal is expressed as anexponential distribution.

FIG. 5 is a graph showing the observed frequency distribution of thenumber of random pulse per 10 seconds generated by amplifying thethermal noises from the resistor of the embodiment of FIG. 1.

FIG. 6 is a graph showing the observed distribution of 8-bit randomnumbers in the embodiment of FIG. 1, where the clock frequency formeasuring the time intervals of random pulse signals is fixed to 11.25MHz and the random number generating speed n per second is changed to beequal to 100 bits, 2,000 bits and 8,000 bits.

FIG. 7 is a schematic circuit diagram of the second embodiment of theinvention.

FIG. 8 is a bar graph, showing the relationship between the decimalrandom numbers and the relative frequency of appearance in theembodiment of FIG. 7.

FIG. 9A is a circuit diagram of a thermal noise element in the form of aresistor having a resistance value of R_(s) and a noninverting amplifierconnected thereto.

FIG. 9B is a circuit diagram of a thermal noise element in the form of adiode having a resistance value of R_(s) and a noninverting amplifierconnected thereto.

FIG. 9C is a circuit diagram of a thermal noise element in the form of aZener diode having a resistance value of R_(s) and a noninvertingamplifier connected thereto.

FIG. 9D is a circuit diagram of a thermal noise element in the form of alight-emitting diode (LED) having a resistance value of R_(s) and anoninverting amplifier connected thereto

FIG. 9E is a circuit diagram of a thermal noise element in the form of atransistor having a resistance value of R_(s) and a noninvertingamplifier connected thereto.

FIG. 9F is a circuit diagram of a thermal noise element in the form ofan inductor having a resistance value of R_(s) and a noninvertingamplifier connected thereto.

FIG. 10 is a graph showing the observed relationship between the pulsepeak value and the frequency in the case of using the resistance valueR_(s) of the thermal noise element and the resistance value R_(f) of theamplifier shown in the figure.

FIG. 11 is distribution graphs showing the relationship between thevalues of the 8 bit random numbers and the frequency of appearancethereof obtained when the resistance value R_(s) of the thermal noiseelement and the resistance value R_(f) of the amplifier are made to varyin the embodiment of FIG. 9.

FIG. 12 is a distribution graph showing the relationship between thevalues of the random numbers and the frequency of appearance thereofobtained when a voltage is applied to the diode of the circuit of FIG. 9from a constant voltage source or a battery.

THE BEST MODE FOR CARRYING OUT THE INVENTION

It is well known that a variety of noises are generated from asemiconductor, a conductor or a resistor when an electric current issupplied to them. These noises include thermal noises generated as aresult of thermal motions of carriers and/or conduction electrons,so-called 1/f noises that are considered to be related to the surfacecondition and the electrical contacts between parts, current noises thatare generated when an electric current is supplied to them (1/f noises)and shot noises that are generated due to fluctuations that arise due tothe fact that the number of carriers and/or electrons is finite.According to the invention, the true random numbers are generated byutilizing the perfectly random phenomenon that are obtained byamplifying the pure thermal noises that arise when no electric currentis supplied to a resistor, a semiconductor or a diode.

The square means value <V²>of the voltages produced by thermal noises isgiven by the formula below:

<V ²>=4kRTB  (formula 1),

where “R” is the resistance value, “k” is the Boltzmann's constant, “T”is the absolute temperature of the resistor and “B” is the frequencybandwidth.

According to the invention, no electric current is supplied to resistorand the thermal noises from the resistor as expressed by formula 1 aboveare amplified and used as random pulse signals, which are then utilizedto generate the true random numbers.

Now, the present invention will be described in detail by referring tothe accompanying drawings that illustrate preferred embodiments of theinvention.

FIG. 1 is a schematic diagram of an embodiment of thermal noise physicalrandom number generator according to the invention, showing its overallconfiguration. Referring to FIG. 1, the thermal noise physical randomnumber generator 1 composes a thermal noise generating element 2 that isany of a resistor, a conductor, a semiconductor element or a diode, apreamplifier 3 connected to one of the terminals of the thermal noisegenerating element 2, a main amplifier 4, a pulse peak discriminator 5for selecting pulse peak of analog pulses amplified by the amplifiershigher than a threshold value, a waveform shaping circuit 6 for shapingthe selected pulses into rectangular waveforms, a clock pulse generator8 for generating clock pulses in order to measure the time between therectangular pulse to the rising edge of the immediately succeedingrectangular pulse, a clock counter 7 for counting the number of clockpulses fed from the clock pulse generator 8 on the basis of n bits(e.g., 8 bits: 256, 10 bits: 1024, etc., n being an integer), a randomnumber generator 9 adapted to read the count value of the clock counter7, a random number storage/controller 10 for storing the random numbersof the random number generator 9.

When a diode is selected as the thermal noise generating element 2, anytype of semiconductor is acceptable. Therefore, an analog switch mightbe a good selection because it is commercially available and it isincorporated easily into an integrated circuit. When, on the other hand,a resistor is used, a large resistance value which to generate largerthermal noises than the noises generated by the preamplifier 3 should beselected in order to remove the 1/f noises from the amplifier 3.

The thermal noise generating element 2 and all the other circuits may beintegrally combined and contained in an IC card or an IC chip. Theoperation of the embodiment will be explained below.

The thermal noises produced from the thermal noise generating element 2without supplying any electric current are amplified and transformedinto analog pulse signals by the preamplifier 3. The analog pulsesignals amplified by the preamplifier 3 are boosted into voltage signalsof several volts for easy detection by the main amplifier 4. Pulsesignals with pulse peak beyond a given pulse peak value are selected bythe pulse peak discriminator 5 out of the voltage signals from the mainamplifier 4 and then shaped into rectangular pulse signals by thewaveform shaping circuit

As the time intervals between the shaped rectangular pulses are random,and whose frequency distribution is expotential. Thus the time intervalsare counted with the time counter 7 that is an n-bit counter (n:integer, e.g., 8-bit counter) by number of clock pulses from the pulsegenerator 8 with frequency of several MHz and the final count number isused as natural random numbers. Then, the random numbers are taken outby the random number generator 9 are stored in the random numberstorage/controller 10. The storage random number are taken out from therandom number storage/controller 10 on external demand.

FIG. 2 is a graph showing the observed pulse peak distribution obtainedby analyzing the analog pulse signals of the thermal noises amplified bythe preamplifier 3 and the main amplifier 4 by means of a pulse peakanalyzer 20, using resistors with different resistance values R_(s)(R_(s)=0, 1 kΩ, 10 kΩ, 20 kΩ, 100 kΩ, 560 kΩ) or a diode fitted as thethermal noise generating element 2 of the embodiment of the embodimentof FIG. 1. As shown in FIG. 2, in case of resistance value of resistoris less than 1 kΩ the thermal noise level from the resistor becomessubstantially same as the noise level of the preamplifier 3. Since thevoltage due to thermal noise is proportional to the square root ({squareroot over (R)}) of the resistance value R of the resistor, the pulsepeak value distribution of the thermal noises of the resistor is foundto be sufficiently larger than that of the noises of the preamplifier 3when a resistance value of more than 100 kΩ is selected for the resistoras seen from FIG. 2.

FIG. 3 is a graph showing the pulse peak value distribution of thethermal noises obtained when a resistor with a resistance value R_(s)=0or 560 kΩ is used as the thermal noise generating element 2. Any desirednumber of pulses per second can be produced by selecting an appropriatethreshold value of the pulse peak discriminator 5 as indicated by arrowsof threshold value A, threshold value B and threshold value C in FIG. 3as so many examples. If, for instance, pulse signals of about 7,650 persecond are generated when the value of arrow A is selected as threshold.Similarly, about 2,800 pulse signals per second are generated when thevalue of allow B is selected as threshold, and about 160 pulse signalsper second are generated when the value of arrow C is selected asthreshold.

The time interval “t” between a pulse signal output from the waveshaping circuit 6 and the pulse signal immediately succeeding thepreceding pulse signal is measured by using clock pulses generated bythe clock pulse generator 8 and the clock counter 7. The time interval“t” is expressed in terms of number of clock pulses. FIG. 4 shows theobserved frequency distribution of time interval “t” in the case ofgeneration speed of 1,000 pulse signals per second that are outputs fromthe wave shaping circuit 6.

As shown in the FIG. 4, the experimental values indicated by the blackdots is expressed by an exponential distribution formula exp. (−t/T₀)shown by the solid line, where T₀ is the average value of the timeintervals “t” and T₀=(1/n)=(1/1,000)=1 millisecond. An arrow in FIG. 4indicates the average value of 1 millisecond. The fact that thefrequency distribution of time intervals of the pulse signals obtainedby amplifying the thermal noises from a resistor is expressed by anexponential distribution indicates that the observed noises represent arandom phenomenon that shows a Poisson distribution. This factguarantees that it is justifiable to use the measured value of the timeinterval of the thermal noise.

When the clock frequency of the clock pulse generator 8 used formeasuring the time interval “t” is F Hz, the unit of time measurement is(1/F) seconds. In other words, the time interval “t” is expressed interms of number of unit time of(1/F). In the measurement of the timeinterval “t” by means of an 8-bit (256) counter, and when the countvalue exceeds 256, that is the time interval is “t”>(256/F), a countingstarting from 1 and ending at 256 is repeated and the residue is used ascount value. Thus, if the count of the time interval “t” is 2,000, forexample, the count value and the random number is 208 because formula“2,000=256×7+208”.

FIG. 5 is a graph of the observed frequency distribution of the numberof pulse signals when the threshold value in the pulse peak distributiongraph of FIG. 3 is fixed so as to make the generation rate of pulsesignals to be equal to 237 per second.

More specifically, the frequency distribution graph of FIG. 5 isobtained by counting the number of pulse signals per 10 seconds for2,000 times.

The average count value (the peak count) of FIG. 5 is 2,370 (or 237 persecond). Then, the standard deviation a is given by σ={square root over( )}(2370)=49. A Gaussian distribution curve having σ value of 49 isalso shown by the broken line curve in FIG. 5. The fact that thefrequency dribution of generation rate of thermal noises from a resistoris a Gaussian distribution certifies that thermal noises from theresistor represent a random phenomenon and hence the thermal noises canbe used as random numbers.

FIG. 6 is a graph of the observed frequency distribution of the 8-bitrandom numbers obtained by measuring the time interval “t” by means of aclock having a clock frequency of 11.25 MHz. In the case of FIG. 6, thegeneration rate of pulse signals is varied from 100 bits per second(12.5 counts per second) to 8,000 bits per second (1,000 counts persecond) by using different threshold values for the pulse peakdiscriminator 5, while fixing the clock frequency to 11.25 MHz. Asclearly seen in FIG. 6, the frequency distribution of random numbersremains substantially uniform even if the generation of pulse signals isvaried remarkably (to a ratio of 80:1).

The voltage produced by the thermal noises from a resistor isproportional to the root of the temperature T of the resistor ({squareroot over (T)}) as indicated by formula 1 above. In other words, even ifthe ambient temperature changes from −60° C. (213K) to +40° C. (313K),the voltage value changes only by about 20%. Thus, as shown in FIG. 6,the influence of the temperature change can be ignored.

A portable physical random number generator that can generate the truerandom numbers at a desired generation speed is fitted to an IC card ora circuit board of a computer or some other device for encoding incomputer telecommunications and for the purpose of personalidentification in mail order business and other commercial transactions.Such a physical random number generator is also used as probabilitygenerator that can eliminate frauds.

FIG. 7 is a schematic circuit diagram of the second embodiment of theinvention that is adapted to generate random numbers by counting thenumber of pulses in a predetermined time period. It comprises a thermalnoise generating element 2, a preamplifier 3, a main amplifier 4, apulse peak discriminator 5 and a waveform shaping circuit 6, which aresame as their counterparts of the embodiment of FIG. 1 and hence willnot be described any further. This embodiment additionally comprises apulse counter 11 for counting the number of pulses in a fixed timeinterval, a decimal random number generator 12 adapted to take out theone-digit number or the several digits number as random number of thecount value of the pulse counter 11 and a random numberstorage/controller 10 for storing the random numbers generated by therandom number generator 12.

The one digit number or the several digits number of the number ofpulses per unit time counted by the pulse counter 11 is used as randomnumber. The following description concerns the case of one-digit numberas random number.

FIG. 8 is a graph of the frequency distribution of the decimal randomnumber of 0 through 9 obtained by using the embodiment of FIG. 7 that isadapted to take out the one digit number as random number. The FIG. 7shows a uniform distribution pattern where 78,000 random numbers aredistributed. In FIG. 8, mark I denotes the one standard deviation. Thus,non-uniformity of FIG. 8 represents the statistical fluctuations.

FIG. 9 is a schematic circuit diagram of a thermal noise generatingelement 2 showing a resistance value of R, and a non-inverting amplifiercircuit connected to the element 2. When the amplifier circuit hasresistors with resistance values of R₀ and R_(f), the gain A of theamplifier circuit is expressed by formula 2 below.

Gain: A=R _(f) /R ₀  (formula 2)

Theoretically, random pulse signals are produced by amplifying theelectromotive force from the thermal noise generating element having aresistance of R_(s) by A (gain) times. However, it is not easy to obtainthe theoretical value because the resistance R_(s) of the thermal noisegenerating element 2 and the resistance R_(f) of the amplifier circuitare mutually dependent

Particularly, the noise generated from the amplifier contains the 1/fnoises and other noises, because an electric current is supplied to theamplifier. Therefore, it is necessary to adjust the relationship betweenthe resistance R_(s) of the thermal noise generating element and theresistance R_(f) of the amplifier circuit so that the noises of theamplifier circuit is negligible. The noises from the amplify mg circuitbecome remarkable and make it difficult to obtain uniform true randomnumbers if a large value is selected for the resistance R, in order toget a high potential from the thermal noise generating element 2 and/orfor the resistance R_(f) in order to get a large gain A, disregardingthe necessary condition in the adjustment.

In view of this fact R_(s)=100 kΩ or 560 kΩ was selected for theresistance of the thermal noise generating element 2 while R_(f)=100 kΩor 560 kΩ was selected for the resistance of the amplifier circuit andthe pulse peak distribution was compared for each combination of theresistance values. In FIG. 10, (1) is the graph obtained for thecombination of R_(s)=100 kΩ and R_(f)=560 kΩ and (2) is the graphobtained for the combination of R_(s)=560 kΩ and R_(f)=560kΩ, whereas(3) is the graph obtained for the combination of R_(s)=560 kΩ andR_(f)=100 kΩ. The pulse peak distributions of these three differentcombinations were obviously different from each other. The pulse peakdistribution of thermal noises due to random thermal motions is apseudo-Boltzmann distribution Eike (1), whereas (2) and (3) show pulsepeak distributions that are totally different from the pseudo-Boltzmanndistribution. From the above result, it is concluded that the primaryrequirement is R_(s)<R_(f) in order to make negligible the contaminationof the noises of the amplifier circuit.

FIG. 11 is distribution graphs showing the frequency distribution of the8-bit random numbers each of the combinations of the resistance valuesdescribed above. The frequency distribution of 8-bit random numbers isuniform for the combination of (1) with one standard deviation of ±34.5to the average value of 1,088 which shows evidence of statisticalfluctuations.

While the combination (2) satisfies the requirement of R_(s)≦R_(f), onestandard deviation of ±120, exceeds far from the level of statisticalfluctuations. The combination (3) of FIG. 10 deviate from the uniformdistribution. Obviously, this is because the case of (3) shows a largeinfluence of the noises from the resistance of R_(f) of the amplifiercircuit.

Generally, it is believed to be difficult to use white noises for randomnumbers because of the noises that enters from the power source. FIG. 12is a distribution graph of the random numbers in which a photodiode isused as the thermal noise generating element 2 and an inverse voltage issupplied to the diode from a constant voltage supply or a battery in thecircuit of FIG. 9 (R_(f)=100 kΩ).

It is obvious from the graph that the uniformity of random numbers isgreatly disturbed by ripples of a constant voltage supply. On the otherhand, the uniformity is retained in the case of a battery for supplyinga voltage.

INDUSTRIAL APPLICABILITY

As describe above, in the random pulse generator and the thermal noisephysical random number generator according to the invention, whitenoises generated from the thermal noise generating element can be useddirectly as random numbers without any modification because no electriccurrent is supplied to the thermal noise generating element unlikecompletely conventional devices and hence they are not influenced by theripples of the power supply and the external noise coming through thepower supply line.

Additional, since the resistance value of the thermal noise generatingelement is selected so that the influence of the amplifier circuitbecome to be negligible, the true physical random numbers can begenerated at a desired random number generating speed by selecting anappropriate threshold value although the random pulse generator and thethermal-noise physical random number generator have a very simplecircuit configuration.

What is claimed is:
 1. A random pulse generator comprising: a thermalnoise generating element having a resistor, a conductor or asemiconductor such as a diode adapted to generate thermal noises withoutapplication of electric current thereto; an analog-amplifier circuit foramplifying the irregular electrical potential generated from the thermalnoise generating element, the analog amplifier circuit coupled to andreceiving thermal noises from the thermal noise generating element; awaveform shaping circuit adapted to take out and taking the output ofthe amplifier circuit as random rectangular pulse signals; and a pulsepeak discriminator adapted to select the pulse peak value of a randompulse as threshold value is connected between the said amplifier circuitand the said waveform shaping circuit.
 2. A random pulse generatoraccording to claim 1, wherein the resistance value R_(s) of resistor ofthe thermal noise generating element is selected less than theresistance value R_(f) of resistor of the said amplifier circuit.
 3. Athermal noise random number generator comprising: a thermal noisegenerating element 2 having a resistor, a conductor or a semiconductorsuch as a diode adapted to generate thermal noises without applicationof electric current thereto; an analog-amplifier circuit for amplifyingthe irregular electrical potential generated from the thermal noisegenerating element, the analog amplifier circuit coupled to andreceiving thermal noises from the thermal noise generating element; awaveform shaping circuit 6 adapted to take out and taking the output ofthe amplifier circuit as random rectangular pulse signals; and an n-bitcounter (n being an integer) for measuring the time interval between arandom pulse signal output from the waveform shaping circuit 6 and theimmediately succeeding random pulse signal, the n-bit counter coupled toand receiving output from the waveform shaping circuit; said thermalnoise random number generator being adapted to output the count of then-bit counter as natural random number.
 4. A thermal noise random numbergenerator comprising: a thermal noise generating element having aresistor, a conductor or a semiconductor such as a diode adapted togenerate thermal noises without application of electric current thereto;an analog-amplifier circuit for amplifying the irregular potentialgenerated from the thermal noise generating element, theanalog-amplifier circuit coupled to and receiving thermal noises fromthe thermal noise generating element; and a waveform shaping circuit 6adapted to take out and taking the output of the amplifier circuit asrandom rectangular pulse signals; the said thermal noise random numbergenerator being adapted to count the number of pulses output from saidwaveform shaping circuit 6 in a predetermined time period and output theone-digit number or the several-digit number as random number.
 5. Athermal noise random number generator according to claim 3 or 4, whereinthe resistance value R_(s) of resistor of the thermal noise generatingelement is selected less than the resistance value R_(f) of the resistorof the said amplifier circuit.
 6. A thermal noise random numbergenerator according to claim 3 or 4, wherein a pulse peak discriminator5 adapted to select the pulse peak value of a random pulse as thresholdvalue is connected between the said amplifier circuit and the saidwaveform shaping circuit
 6. 7. A thermal noise physical random numbergenerator according to any of claim 3 through 6, wherein the thermalnoise generator 2 that is a resistor or a diode is contained integrallywith other circuits in an IC card or an IC chip provided with aninformation processing circuit and the information processing circuitare fed with physical random numbers for the purpose of personalidentification, coding and other purposes in computer telecommunicationsor internet sales or for using it as probability generator in a gamemachine.